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<html>
<head>
<title>
SPHERE_TRIANGLE_MONTE_CARLO - Monte Carlo Estimates of Integrals over Spherical Triangles
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
SPHERE_TRIANGLE_MONTE_CARLO <br> Monte Carlo Estimates of Integrals over Spherical Triangles
</h1>
<hr>
<p>
<b>SPHERE_TRIANGLE_MONTE_CARLO</b>
is a FORTRAN90 library which
applies the Monte Carlo method to estimate the integral of a function $f(x,y,z)$
over a spherical triangle.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this
web page are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/random_data/random_data.html">
RANDOM_DATA</a>,
a FORTRAN90 library which
generates sample points for
various probability distributions, spatial dimensions, and geometries;
</p>
<p>
<a href = "../../f_src/sphere_cvt/sphere_cvt.html">
SPHERE_CVT</a>,
a FORTRAN90 library which
creates a mesh of well-separated points on a unit sphere using Centroidal Voronoi
Tessellations.
</p>
<p>
<a href = "../../f_src/sphere_delaunay/sphere_delaunay.html">
SPHERE_DELAUNAY</a>,
a FORTRAN90 program which
computes and plots the Delaunay triangulation of points on the unit sphere.
</p>
<p>
<a href = "../../f_src/sphere_design_rule/sphere_design_rule.html">
SPHERE_DESIGN_RULE</a>,
a FORTRAN90 library which
returns point sets on the surface of the unit sphere, known as "designs",
which can be useful for estimating integrals on the surface, among other uses.
</p>
<p>
<a href = "../../f_src/sphere_exactness/sphere_exactness.html">
SPHERE_EXACTNESS</a>,
a FORTRAN90 program which
tests the polynomial exactness of a quadrature rule for the unit sphere;
</p>
<p>
<a href = "../../f_src/sphere_grid/sphere_grid.html">
SPHERE_GRID</a>,
a FORTRAN90 library which
provides a number of ways of generating grids of points, or of
points and lines, or of points and lines and faces, over the unit sphere.
</p>
<p>
<a href = "../../f_src/sphere_lebedev_rule/sphere_lebedev_rule.html">
SPHERE_LEBEDEV_RULE</a>,
a FORTRAN90 library which
computes Lebedev quadrature rules for the unit sphere;
</p>
<p>
<a href = "../../f_src/sphere_monte_carlo/sphere_monte_carlo.html">
SPHERE_MONTE_CARLO</a>,
a FORTRAN90 library which
applies a Monte Carlo method to estimate the integral of a function
over the surface of the sphere in 3D;
</p>
<p>
<a href = "../../f_src/sphere_quad/sphere_quad.html">
SPHERE_QUAD</a>,
a FORTRAN90 library which
approximates an integral over the surface of the unit sphere
by applying a triangulation to the surface;
</p>
<p>
<a href = "../../f_src/sphere_triangle_quad/sphere_triangle_quad.html">
SPHERE_TRIANGLE_QUAD</a>,
a FORTRAN90 library which
estimates the integral of a function over a spherical triangle using quadrature.
</p>
<p>
<a href = "../../f_src/sphere_voronoi/sphere_voronoi.html">
SPHERE_VORONOI</a>,
a FORTRAN90 program which
computes the Voronoi diagram of points on a sphere.
</p>
<p>
<a href = "../../f_src/stripack/stripack.html">
STRIPACK</a>,
a FORTRAN90 library which
computes the Voronoi diagram or Delaunay
triangulation of pointsets on a sphere.
</p>
<p>
<a href = "../../f_src/stroud/stroud.html">
STROUD</a>,
a FORTRAN90 library which
approximates the integral of a function on the surface or in the interior
of a variety of geometric shapes.
</p>
<p>
<a href = "../../m_src/xyz_display/xyz_display.html">
XYZ_DISPLAY</a>,
a MATLAB program which
reads XYZ information defining points in 3D,
and displays an image in the MATLAB graphics window.
</p>
<p>
<a href = "../../cpp_src/xyz_display_opengl/xyz_display_opengl.html">
XYZ_DISPLAY_OPENGL</a>,
a C++ program which
reads XYZ information defining points in 3D,
and displays an image using OpenGL.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ul>
<li>
Jacob Goodman, Joseph ORourke, editors,<br>
Handbook of Discrete and Computational Geometry,<br>
Second Edition,<br>
CRC/Chapman and Hall, 2004,<br>
ISBN: 1-58488-301-4,<br>
LC: QA167.H36.
</li>
</ul>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "sphere_triangle_monte_carlo.f90">sphere_triangle_monte_carlo.f90</a>, the source code.
</li>
<li>
<a href = "sphere_triangle_monte_carlo.sh">sphere_triangle_monte_carlo.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "sphere_triangle_monte_carlo_prb.f90">sphere_triangle_monte_carlo_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "sphere_triangle_monte_carlo_prb.sh">sphere_triangle_monte_carlo_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "sphere_triangle_monte_carlo_prb_output.txt">sphere_triangle_monte_carlo_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>ARC_COSINE</b> computes the arc cosine function, with argument truncation.
</li>
<li>
<b>MONOMIAL_VALUE</b> evaluates a monomial.
</li>
<li>
<b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</li>
<li>
<b>R8VEC_NORM</b> returns the L2 norm of an R8VEC.
</li>
<li>
<b>R8VEC_NORMALIZE</b> normalizes an R8VEC in the Euclidean norm.
</li>
<li>
<b>SPHERE01_SAMPLE</b> picks random points on the unit sphere.
</li>
<li>
<b>SPHERE01_TRIANGLE_ANGLES_TO_AREA:</b> area of a triangle on the unit sphere.
</li>
<li>
<b>SPHERE01_TRIANGLE_SIDES_TO_ANGLES:</b> angles of triangle on unit sphere.
</li>
<li>
<b>SPHERE01_TRIANGLE_VERTICES_TO_AREA:</b> area of triangle on unit sphere.
</li>
<li>
<b>SPHERE01_TRIANGLE_VERTICES_TO_SIDES:</b> sides of triangle on unit sphere.
</li>
<li>
<b>SPHERE01_TRIANGLE_SAMPLE:</b> sample spherical triangle on unit sphere.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 06 February 2012.
</i>
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